If K is a finite-dimensional metric compact space, then L(K) is embedded in L(0) as a

topological vector space.

Suppose X is a locally convex

topological vector space equipped with original topology T as well as weak topology [T.sub.w]; and (WCC (X) ;[T.sub.w]) is the corresponding hyperspace.

(Park [24]) Let X be a nonempty convex subset of a locally convex Hausdorff

topological vector space E and F : X [??] X be an acyclic map.

Seoane-Sepulveda, Linear subsets of nonlinear sets in

topological vector spaces, Bull.

The next result extends Proposition 3.1 of [10] from normed linear spaces to metrizable

topological vector spaces.

Then it is a

topological vector space iff [[alpha].sub.p] = 0 for all p [member of] V.

A topological algebra (or a

topological vector space) A is called a galbed algebra (a galbed space) if there exists a sequence ([[alpha].sub.n]) [member of] l such that for every neighbourhood O of zero in A there exists a neighbourhood U of zero in A such that

Let Z and W be subsets of Hausdorff

topological vector spaces [Y.sub.1] and [Y.sub.2] and F a multifunction.

Given a subset H of a

topological vector space E, a closed real hyperplane M is called a supporting hyperplane of H, if H [intersection] M [not equal to] [empty set] and H lies in one of the two closed half-spaces defined by M, while the elements of H [intersection] M are called points of support of H.

Katsaras, "Fuzzy

topological vector spaces. II," Fuzzy Sets and Systems, vol.

Given a real Hausdorff

topological vector space E, a closed convex set X [[subset].bar] E, and an operator [PHI] : X [right arrow] E*, the problem of finding x [member of] X in such a way that

Among the topics are coincidence and fixed points of fuzzy mappings, topological monads from functional quasi-uniformities, topological entropy and algebraic entropy for group endomorphisms, some problems in isometrically universal spaces, and the

topological vector space of continuous functions with the weak set-open topology.